Participants

Photos by Hope Prosser from Kiama Council

Attendees of the meeting are listed below. Click on a talk title to see the abstract.

Luis Fernando Alday	The analytic conformal bootstrap
	A conformal field theory is characterised by the CFT data, namely the spectrum of scaling dimensions and OPE coefficients. The idea of the conformal bootstrap is to use associativity of the operator algebra together with the symmetries of the theory to constraint the CFT data. For the sector of operators with large spin one can actually use these ideas to obtain analytical results. We will explain how to set up a "large spin perturbation theory", namely a systematic expansion around the large spin sector, leading to analytic results to all orders in inverse powers of the spin. This allows to obtain analytic results for vast families of CFTs, including vector models, weakly coupled gauge theories and the computation of loops for scalar theories in AdS.
Fahad Alshammari	Casimir operator of Galilean conformal algebra and related structures
	Casimir operators of Lie algebras play an important role in both representation theory and physical applications. The Casimir operators for semisimple Lie algebras are well-known, but for non-semisimple Lie algebras the situation can be more complicated. Although several methods and algorithms have been developed over the years that produce Casimir operators in such cases, many have their computational challenges. In my talk, I will outline some ideas developed in my project that form the heart of a new algorithm to produce Casimir operators. I will demonstrate the algorithm in the context of the family of finite-dimensional conformal Galilei algebras. Joint work with Phillip S Isaac, UQ; Dr. Ian Marquette, UQ.
Michael Baake	Reversing and extended symmetries of shift spaces
	The reversing symmetry group is considered in the setting of symbolic dynamics. While this group is generally too big to be analysed in detail, there are interesting cases with some form of rigidity where one can determine all symmetries and reversing symmetries explicitly. They include Sturmian shifts as well as classic examples such as the Thue--Morse system with various generalisations or the Rudin--Shapiro system. We also look at generalisations of the reversing symmetry group to higher-dimensional shift spaces, then called the group of extended symmetries. We develop their basic theory for faithful shift actions, and determine the extended symmetry group of the chair tiling shift, which can be described as a model set, and of Ledrappier's shift, which is an example of algebraic origin. Joint work with John A G Roberts, and Reem Yassawi.
Murray Batchelor	Spectral statistics of the quantum Rabi model
	The quantum Rabi model describes the fundamental interaction between light and matter, more specifically, between a qubit and a single boson mode of a quantised light field [1]. In this talk I will discuss some recent progress on the spectral statistics of this model, an aspect which has received relatively little attention. [1] D. Braak, Q.-H. Chen, M.T. Batchelor and E. Solano, Semi-classical and quantum Rabi models: in celebration of 80 years, J. Phys. A 49, 300301 (2016)
Vladimir Bazhanov	Bukhvostov-Lipatov model and duality of quantum and classical systems
	Bukhvostov and Lipatov have shown that weakly interacting instantons and anti-instantons in the O(3) non-linear sigma model in two dimensions are described by an exactly soluble model containing two coupled Dirac fermions. We propose an exact formula for the vacuum energy of the model for twisted boundary conditions, expressing it through a special solution of the classical sinh-Gordon equation. The formula perfectly matches predictions of the standard renormalized perturbation theory at weak couplings as well as the conformal perturbation theory at short distances. A complete proof the proposed expression for the vacuum energy is based on a combination of the Bethe ansatz techniques and the classical inverse scattering transform method. The description of the vacuum state of the quantum model in terms of the classical sinh-Gordon equation can be viewed as an instance of a remarkable, albeit unusual correspondence between integrable quantum field theories and integrable classical field theories in two dimensions, which cannot be expected from the standard quantum–classical correspondence principle.
Nicholas Beaton	Characterizing knotting for polymers in nanochannels
	We model long ring polymers in a thin channel, using self-avoiding polygons in a tubular sublattice of the simple cubic lattice, and use transfer-matrix and Monte Carlo methods to study their topological properties. In particular, we consider different ways of defining the “size” of a knot relative to the length of the polymer, and find that the distribution of knot sizes is heavily dependent on the definition used. The relevance of these results to recent experiments involving DNA knots in solid-state nanopores will also be discussed. Joint work with Christine E Soteros and Jeremy W Eng.
Peter Bouwknegt	Higher spin algebras and representation theory
	In this talk I will discuss higher spin algebras from the point of view of universal enveloping algebras and their ideals.
Richard Brak	Affine refections, division algebras and solvability of quarter plane random walk problems
	I will show how reflection groups and affine reflection groups provide a geometric understanding of why certain quarter plane random walk models can or cannot be solved (by a certain class of methods). Additionally the relationship between rational map path groups and divisions rings will be given. The latter relationship will give a geometric understanding of the rational maps.
Mark Bugden	It's T-duality, but not as we know it
	T-duality is a procedure for assigning to a Riemannian manifold with an abelian group of isometries another Riemannian manifold called the dual manifold. This dual manifold has the property that when used as a string background, it is physically indistinguishable from the original background. This notion has been generalised to Riemannian manifolds with a nonabelian group of isometries, and much more recently, to backgrounds without any isometries (but with some milder conditions). I will discuss work towards some new examples of this generalised T-duality.
Joshua Capel	Generalizations of the Askey-Wilson Algebra and multivariate orthogonal polynomials
	This talk will briefly discuss recent results regarding generalisation of the Askey-Wilson algebra and associated orthogonal polynomials (Joint work with Sarah Post)
Michael Cromer	Free Field Realisations of Logarithmic Conformal Field Theories
	The symmetries of conformal field theory actually allow for the presence of logarithmic terms in correlation functions. In the last twenty years, many physically interesting examples of logarithmic theories have been found, notably including statistical models such as percolation and dilute polymers. State spaces associated to logarithmic theories exhibit non-diagonalisable action of the Virasoro algebra, and their construction has been approached in the literature by 'gluing' two highest weight Virasoro representations together in a nontrivial way. This talk presents recent work in applying this technique to Fock spaces in the hope of finding realisations of these representations in terms of the free boson. We will also see how logarithmic behaviour at the field level might correspond simply to an extension of the algebra at the mode level.
Jan De Gier	Rigorous finite-size corrections for universal boundary entropy in bond percolation
	We compute the boundary entropy for bond percolation on the square lattice in the presence of a boundary loop weight, and prove explicit and exact expressions on a strip and on a cylinder of size L. For the cylinder we provide a rigorous asymptotic analysis which allows for the computation of finite-size corrections to arbitrary order. For the strip we provide exact expressions. Our rigorous and exact results corroborate an argument based on conformal field theory, in particular concerning universal logarithmic corrections for the case of the strip due to the presence of corners in the geometry. We furthermore observe a crossover at a special value of the boundary loop weight. Joint work with Jesper Jacobsen and Anita Ponsaing.
Youjin Deng	Emergent O(n) symmetry in a series of three-dimensional Potts models
	We study the q-state Potts model on a simple cubic lattice with ferromagnetic interactions in one lattice direction, and antiferromagnetic interactions in the other two directions. As the temperature T decreases, the system undergoes a second-order phase transition that fits in the universality class of the three-dimensional O(n) model with n = q − 1. This conclusion is based on the estimated critical exponents, and histograms of the order parameter. At even smaller T we find, for q = 4 and 5, a first-order transition to a phase with a different type of long-range order. This long-range order dissolves at T = 0, and the system effectively reduces to a disordered two-dimensional Potts antiferromagnet. These results are obtained by means of Monte Carlo simulations and finite-size scaling.
Andrew Elvey Price
Omar Foda	A Macdonald refined topological vertex
	We consider the refined topological vertex as a function of two parameters, x and y, and refine it further by introducing two Macdonald-type parameters, q and t. We explain the relation of the new topological vertex to Ding-Iohara-Miki algebra, and conjecture an elliptic extension related to Saito's elliptic algebra. Joint work with J F Wu (Beijing).
John Foxcroft	Osculating paths, the six-vertex model and Malcev-Neumann rings: Constant terms of Rational functions
	Osculating paths are sets of non-crossing directed lattice paths, which are allowed to share vertices, but not edges. They have combinatorial links to the six-vertex model as well as the alternating sign matrix problem. I will outline a constant term formula for the number of these paths, and discuss the relationship between the constant term of a rational function and the choice of Malcev-Neumann ring.
Joerg Frauendiener	On the computation of Theta functions on Riemann surfaces
	Theta functions are often used in the solution of integrable systems such as the KdV, non-linear Schrödinger and KP equations. In order to study the properties of the solutions these functions have to be computed. In this talk I will present joint work with Christian Klein on how to completely determine the Theta functions given only an algebraic curve as initial datum.
Alexandr Garbali
Timothy Garoni	Critical Speeding-up in Percolation
	We prove the existence of "critical speeding-up" for the mean cluster size in two-dimensional and high-dimensional percolation. More precisely, we prove that the dynamical critical exponent of the corresponding integrated autocorrelation time is negative for dynamical bond percolation on high dimensional tori, and on the triangular lattice. The proof of the latter harnesses recent rigorous results on the conformal invariance of critical site percolation on the triangular lattice. Joint work with Andrea Collevecchio, Eren Elci, and Greg Markowsky.
Rod Gover	New invariants via renormalised volume
	We develop a very general and simplified approach to renormalized volume for conformally compact manifolds and show that this reveals new global invariants in conformal manifolds. Joint work with Andrew Waldron.
Jens Grimm	Geometric explanation of anomalous finite-size scaling in high dimensions
	Finite-size scaling (FSS) is a fundamental physical theory within statistical mechanics, describing the asymptotic approach to the thermodynamic limit of finite systems in the neighbourhood of a critical phase transition. It is well-known that models of critical phenomena typically possess an upper critical dimension, d_c, such that in dimensions d > d_c, their thermodynamic behaviour is governed by critical exponents taking simple mean-field values. In contrast to the simplicity of the thermodynamic behaviour, however, the theory of FSS in dimensions above d_c is surprisingly subtle, and remains the subject of ongoing debate. We will argue that such subtleties can be explained in a simple way, by taking an appropriate geometric perspective. Our picture is supported by Markov-chain Monte Carlo simulations of the Ising model and self-avoiding walk on five-dimensional hypercubic lattices. Joint work with Eren M. Elci, Zongzheng Zhou, Tim Garoni, and Youjin Deng.
Tony Guttmann	Pattern-avoiding permutations
	Pattern-avoiding permutations (PAPs) play a key role in several combinatorial structures that arise in mathematical physic and theoretical computer science. The number of classical PAPs are known to grow exponentially, and solved cases grow as p_n(π) ~ const. × mⁿ × n^g, where p_n is the number of permutations of length n that avoid the sub-permutation π, called a pattern. By contrast, the number of consecutive PAPs, c_n(π) are believed to grow as c_n(π) ~ const. × n! × mⁿ × n^g. We describe these two families and present new results for both classical and consecutive PAPs.
Phillip Isaac	Matrix elements for type 2 unitary irreducible representations of the Lie superalgebra gl(m\|n)
	We discuss the characteristic identity formalism and outline its utlity in deriving matrix elements for the type 2 unitary representations of gl(m\|n). We also consider the notion of duality in this context.
Peter Jarvis	Plethystic vertex operators and boson-fermion correspondences
	We study the algebraic properties of plethystic vertex operators, introduced in (2010 J. Phys. A: Math. Theor. 43 405202), underlying the structure of symmetric functions associated with certain generalized universal character rings of subgroups of the general linear group, defined to stabilize tensors of Young symmetry type characterized by a partition of arbitrary shape π. Here we establish an extension of the well-known boson-fermion correspondence involving Schur functions and their associated (Bernstein) vertex operators: for each π, the modes generated by the plethystic vertex operators and their suitably constructed duals, satisfy the anticommutation relations of a complex Clifford algebra. The combinatorial manipulations underlying the results involve exchange identities exploiting the Hopf-algebraic structure of certain symmetric function series and their plethysms. J. Phys. A: Math. Theor. 49 (2016) 425201. Joint work with Bertfried Fauser and Ronald King.
Iwan Jensen	Three friendly walkers
	More than 15 years ago Guttmann and Vöge [J. Statist. Plann. Inference, 101, 107 (2002)], introduced a model of friendly walkers. Since then it has remained unsolved. We provide the exact solution to a closely allied model which essentially only differs in the boundary conditions. The exact solution is expressed in terms of the reciprocal of the generating function for vicious walkers which is a D-finite function. However, ratios of D-finite functions are inherently not D-finite and in this case we prove that the friendly walkers generating function is the solution to a non-linear differential equation with polynomial coefficients, it is in other words D-algebraic. We find using numerically exact calculations a conjectured expression for the generating function of the original model as a ratio of a D-finite function and the generating function for vicious walkers. We obtain an expression for this D-finite function in terms of a hypergeometric function with a rational pullback and its first and second derivatives.
Andrew Kels	The star-triangle relation, lens partition function, and hypergeometric sum/integrals
	The star-triangle relation (STR) is a fundamental relation for integrability of two-dimensional lattice models of statistical mechanics, that first arose over 72 years ago in Onsager's solution of the 2-d Ising model. In the last decade or so, it has become evident that STR is also a key relation for several other areas of mathematical physics, and provides new correspondences from the latter areas to integrable lattice models. Such correspondences are a powerful tool for gaining insight into the different areas that are connected through STR. This talk will give an overview of such correspondences between the three areas of integrable lattice models, elliptic hypergeometric functions, and supersymmetric gauge theory, and the latest results comprising the most general known solutions of STR. Joint work with Ilmar Gahramanov.
Slaven Kozic	Center of the quantum affine vertex algebra in type A
	By the results of P. Etingof and D. Kazhdan, the vacuum module V_c(gl_N) for the double Yangian DY(gl_N) has a quantum vertex algebra structure. We will introduce the definition of the center of an arbitrary quantum vertex algebra and recall some of its properties. Finally, we will present our main result, the explicit description of the center of the quantum vertex algebra V_c(gl_N) at the critical level c=-N. This is a joint work with N. Jing, A. Molev and F. Yang. Joint work with Naihuan Jing, Alexander Molev, and Fan Yang.
Bernd Krauskopf	Delay-induced dynamics: mode structure of a semiconductor laser with two filtered feedback loops
	Delays arise in many areas, including control theory, communication systems, electrodynamics and laser physics. When they are sufficiently large with respect to the internal time scales of the system under consideration, delays need to be taken into account in the mathematical description. This leads to models in the form of delay-differential equations, which are a special class of infinite-dimensional dynamical systems. The talk will demonstrate how advanced methods from dynamical systems can be brought to bear to gain insight into the overall dynamics of systems with delays. Specifically, the talk will present a case study of a semiconductor laser receiving time-delayed and frequency-filtered optical feedback (FOF) from two external filters. This system is referred to as the 2FOF laser, and it has been used as pump laser in optical telecommunication and as light source in sensor applications. Our analysis of the 2FOF laser focuses on the basic solutions of the underlying DDE, known as external filtered modes (EFMs), which correspond to laser output with steady amplitude and frequency. We consider the EFM-surface in the space of steady-state frequency, the corresponding steady-state population inversion, and the feedback phase difference. The EFM-surface emerges as a natural object, because it allows us to give a complete classification of the EFM structure in dependence on system parameters, including the detunings and width of the filters and the two delay times. To achieve this, we employ singularity theory in conjunction with continuation methods to determine how the parameter space is divided into regions of geometrically different types of EFM surface. Finally, we show that there are bands and islands of stability related to the type of EFM-surface that may be accessible and distinguishable experimentally. This is joint work with Poitr Slowinski, University of Exeter, and Sebastian Wieczorek, University College Cork.
Jonathan Kress
Jon Links
Elynor Liu	Asymptotic Behaviours of Painlevé V
	In this talk, we begin by reviewing some properties of Painlevé equations in the continuous and discrete domain. We then specialise to studying the elliptic asymptotic behaviour of Painlevé V and its discrete counter part (D₅⁽¹⁾ surface type) near infinity in the independent variable. We then connect this elliptic function locally, that is we analyse the evolution of E (the energy-like parameter) by an averaging method.
Tianshu Liu	Towards N=2 Minimal Models
	Conformal field theory is an essential tool of modern mathematical physics with applications to string theory and to the critical behaviour of statistical lattice models. The symmetries of a conformal field theory include all angle-preserving transformations. In two dimensions, these transformations generate the Virasoro algebra, a powerful symmetry that allows one to calculate observable quantities analytically.The symmetries of a conformal field theory may be strictly larger than the Virasoro algebra. One possibility which is crucial importance to string theory applications is that of supersymmetry, where the Virasoro algebra is extended by a given number of fermionic fields. The talk aims to explain certain aspects of N=2 superconformal field theory using the arsenal of mathematical technology and physical insight that has been built up over the last five years.
Xin Liu	On the derivation of HOMFLYPT as a new invariant of topological fluid mechanics
	When unlinked, unknotted vortex loops are formed helicity may fail to detect topological complexity accurately. By using and extending earlier results (Liu & Ricca 2012), we derive the skein relations of the HOMFLYPT polynomial for ideal fluid knots from helicity, thus providing a rigorous proof that the HOMFLYPT polynomial is a new, powerful invariant of topological fluid mechanics (Liu & Ricca 2015). Since this invariant is a two-variable polynomial, the skein relations are derived from two independent equations expressed in terms of writhe and twist contributions. Writhe is given by addition/subtraction of imaginary local paths, and twist by Dehn's surgery. HOMFLYPT then becomes a function of knot topology and field strength. For illustration we derive explicit expressions for some elementary cases and apply these results to homogeneous vortex tangles. Recently, by using this method, we prove that each stage of a cascade process, that follows a complexity-reducing path given by a sequence of T(2,2n+1) torus knots and T(2,2n) torus links produced by consecutive reconnections, can be detected by a unique, monotonically decreasing sequence of HOMFLYPT numerical values (Liu & Ricca 2016). This opens the doors to useful applications in the study of the decay process of classical and quantum vortex tangles. References: Liu, X. & Ricca, R.L. (2012) The Jones polynomial for fluid knots from helicity. J. Phys. A: Math. & Theor. 45, 205501. Liu, X. & Ricca, R.L. (2015) On the derivation of HOMFLYPT polynomial invariant for fluid knots. J. Fluid Mech. 773, 34-48. Liu, X. & Ricca, R.L. (2016) Knots cascade detected by a monotonically decreasing sequence of values, Sci. Rep. 6, 24118. Joint work with Renzo L. Ricca.
Inna Lukyanenko
Vladimir Mangazeev	Integrable structure of products of finite Ginibre random matrices
	We study the squared singular values of the product of M complex Ginibre matrices which form a determinantal point process with correlation kernel given by Meijer's G-functions. It was shown by Strahov that a hard edge scaling limit is described by Hamiltonian differential equations which can be formulated as the isomonodromic deformation system similar to the theory of Jimbo, Miwa, Mori, Ueno and Sato. We generalize this result to the case of finite matrices and find a new representation of the finite correlation kernel in terms of biorthogonal functions. As a result we obtain the Hamiltonian structure for a finite size matrices and formulate it in terms of (M+1)x(M+1) matrix Schlezinger system. The case M=1 reproduces the Tracy and Widom theory which results in the Painleve V equation for the gap probability.
Ian Marquette	Superintegrable models: background, ideas and new developments
	We review recent results of systematic searches for superintegrable by different approaches and discuss the connection with special functions and finitely generated polynomial algebras.
Anthony Mays	Finite-size corrections in random matrix theory and the Riemann zeros
	Assuming the Riemann hypothesis is true (that all the non-trivial zeros of the Riemann zeta function lie on the line z = 1/2 +i s) we can look to describe the distribution of the zeros on the critical line. The Montgomery-Odlyzko conjecture claims that the statistics of the zeros (a large distance from the real axis) match those of the eigenvalues of certain (large dimensional) random matrix ensembles. We discuss how the leading order and first correction terms of the eigenvalue spacings in the random matrix ensembles can be characterized as Fredholm determinants and as Painlevé transcendents, and we then compare these to the data of the Riemann zeros, finding very good agreement.
William Moore	The Asymmetric Simple Exclusion Process, bi-orthogonality and Askey-Wilson polynomials
	I will state the diffusion algebra equations of the stationary state of the five parameter (α, β, γ, δ and q) Asymmetric Simple Exclusion Process as a linear functional L, acting on a tensor algebra. From L a pair of sequences of monic polynomials are constructed which are bi-orthogonal. The action of these polynomials on the boundary vector gives a basis which is associated with the Askey-Wilson polynomials obtained by Sasamoto.
Nobutaka Nakazono	Elliptic Painlevé equations
	Elliptic Painlevé equations head the list of the differential and discrete Painlevé equations. In 2009, an elliptic Painlevé equation is reported by Ramani, Carstea and Grammaticos. In this talk, we show the geometry of this equation: its space of initial values and corresponding Cremona isometries. Moreover, using this geometrical setting we derive two new elliptic Painlevé equations. This work has been supported by an Australian Laureate Fellowship #FL120100094 and grant #DP160101728 from the Australian Research Council. Joint work with Nalini Joshi.
Jeremy Nugent	Classifying superintegrable pp-waves
	The pp-wave spacetimes are 4D metrics which arise in General Relativity. We discuss their symmetry properties, showing that a large subset of these metrics are superintegrable (have maximal symmetry) and analyse their symmetry algebras.
Todd Oliynyk	A priori estimates for relativistic liquid bodies
	The timelike matter-vacuum boundary for fluid bodies with compact support is defined by the vanishing of the pressure. Due to the free nature of the boundary, obtaining estimates near the boundary without a loss of derivatives is technically challenging. In this talk, I will present a new wave formulation for the relativistic Euler equations that is especially suited to obtaining estimates in the presence of a fluid boundary, and importantly, does not require the liquid to be irrotational.
Paul Pearce
Thomas Quella	Haldane phases of SU(N) spin chains and how to realize them in cold-atom gases
	Historically, the Haldane phase in S=1 SU(2) spin chains is one of the first examples of a symmetry-protected topological phase. In this talk, I will discuss the classification of symmetry-protected topological phases for spin systems with continuous symmetry, specifically SU(N), and show how these can be realised in cold atom gases.
Milena Radnovic	Asymptotic behaviour of fourth Painleve transcendents
	We study the asymptotic behaviour of solutions of the fourth Painleve equation as the independent variable goes to infinity in its space of (complex) initial values, which is a generalisation of phase space described by Okamoto. We show that the limit set of each solution is compact and connected and, moreover, that any non-special solution has an infinite number of poles and infinite number of zeroes. Joint work with Nalini Joshi.
Eric Ragoucy	Integrability in out-of-equilibrium systems
	Out-of-equilibrium systems have nowadays an important role in 1d statistical physics. Although an equilibrium state obviously doesn’t exist for such systems, one looks for a steady state (that is stationary in time). It is defined as the zero-eigenvalue eigenstate of the Markov matrix that describe the systems. Its exact computation is at the core of many researches. In some cases, the matrix product state ansatz (matrix ansatz for short) allows to compute this steady state. However no general approach for this ansatz is known. On the other hand, many 1d statistical models appear to be integrable, which allows to get eigenstates of the Markov matrix through Bethe ansatz. The goal of this presentation is to show how integrability gives a natural framework to construct the matrix ansatz for 1d systems with boundaries. It can be done on very general grounds, allowing to construct the matrix ansatz when it is not known, and also to define new models and/or to find boundary conditions ‘adapted’ to the model under consideration. We will illustrate the technique on some examples.
Christopher Raymond	Galilean contractions of W-algebras
	We investigate Galilean contractions of operator product algebras. We show that several families of algebras such as the N=1,2, and 4 superconformal algebras, and affine Kac-Moody algebras admit Galilean contractions, as well as their compatibility with other established algebra constructions. Furthermore, we discuss Galilean contractions of W-algebras and provide evidence for the existence of a new class of W-algebras. Joint work with Jorgen Rasmussen.
Adam Rennie	The bulk-edge correspondence for topological insulators
	Topological phases of matter are characterised by robust invariants of the material associated to boundary ``currents''. In this talk I will show how to relate bulk invariants with edge invariants. Joint work with Chris Bourne (Erlangen and Sendai), Alan Carey (ANU and Wollongong) and Johannes Kellendonk (Lyon).
David Ridout
John A G Roberts	Driven linear dynamics over finite fields
	We introduce a class of dynamical systems over finite fields which are specified by a finite collection of linear maps, which are driven by words of low (affine) complexity. We use various approaches to study recurrence and transitions on the directed graphs induced by the dynamics of the finite state space. Joint work with Franco Vivaldi.
Boris Runov	On spectral problem of integrable Quantum Field Theory
	We study ODE/IM correspondence in QFT on the example of Lipatov-Boukhvostov model. We associate with QFT a second order differential equation with 3 singular points arising from linear problem for modified sinh-Gordon equation. Functional equations on connection matrices manifesting the symmetry of ODE w.r.t. rotation around singularities give rise to Bethe Ansatz type equations which are interpreted as Bethe Ansatz equations for Lipatov-Boukhvostov model. Using analytical properties of connection matrices we derive a system of nonlinear integral equations, which can be solved numerically. We compute vacuum energy of the model and check our results against asymptotical expressions obtained using perturbation theory.
Tomohiro Sasamoto	Exact solutions of 1D KPZ equation and related models
	The KPZ equation is a non-linear stochastic partial differential equation introduced by Kardar, Parisi, Zhang in 1986 to describe dynamics of interface. Its one-dimensional version already shows interesting scaling behaviors characterized by the exponent 1/3, which suggests non-Gaussian fluctuations. In 2010, the exact solution for the height distribution for the 1D KPZ equation was discovered by TS-Spohn and Amir-Corwin-Quastel. There have been vast developments in the field since then. It has turned out that the solvability of the 1D KPZ equation is related to various models of quantum integrable systems such as the free fermion, XXZ spin chain, q-boson models, quantum Tora lattice, Macdonald polynomials and so on. In this presentation, after discussing these developments, we present our recent analysis of a certain model (q-TASEP) using Ramanujan’s summation formula and the Cauchy identity for the theta function. References [1] T. Sasamoto, The 1D Kardar-Parisi-Zhang equation: Height distribution and universality, Prog. Theor. Exp. Phys. 022A01 (2016). [2] T. Imamura, T. Sasamoto, Fluctuations for stationary $q$-TASEP, in preparation.
Susan Scott	LIGO and the Dawn of the Age of Gravitational Wave Astronomy
	This talk will provide an overview of the first direct detection of gravitational waves and gravitational wave astronomy. The 100 years of discoveries and endeavours leading to the first direct detection of gravitational waves will be summarised, highlighting the extraordinary difficulty of the quest to detect them and the many obstacles, both experimental and theoretical, which needed to be overcome along the way. The details and significance of the first detection (and subsequent detections) will be presented. Aspects of the new field of gravitational wave astronomy will be discussed.
Yibing Shen	Analysis of exact solutions for the p+ip pairing Hamiltonian.
	In this talk, we discuss a two-dimensional BCS model where the symmetry of the pairing interaction is p+ip-wave. This model dates back to the original study of the BCS model describing superconductivity and rose to prominence in identifying topological properties of superconducting systems. This model was shown to be exactly solvable in 2009. We will focus on techniques to analyse the behaviour of the ground-state Bethe roots and energy for large systems corresponding to various parameter regimes. We also examine under what conditions our methods may be applied. Further, we outline an alternative approach to analysing the Bethe roots via polynomials and present related results.
Somayeh Shiri	Rigorous construction of the effective description of TASEP on a ring via Bethe ansatz
	Studying large deviation functions (LDF) in non-equilibrium statistical mechanics typically relies on simulation. Simulation of rare events is a notoriously difficult task however. In the past decade, a number of advanced Monte Carlo techniques have been introduced to investigate the LDF of macroscopic observables in non-equilibrium statistical mechanics. The Iterative Measurement-and-Feedback method is a powerful method introduced recently in [1]. For this method to be feasible in practice, it needs to be augmented with a so-called "effective description" of the system being studied. Such effective descriptions have been conjectured and tested numerically, for a number of models including TASEP. In this talk we use Bethe ansatz to construct, and rigorously justify the effective description of TASEP on a ring. Joint work with Timothy M. Garoni.
Steve Siu
Arthur Suvorov	Gravitational waves and causality in modified gravity
	In the theory of general relativity (GR), gravitational wave-fronts trace out null hypersurfaces. As such, the notions of electromagnetic and gravitational causality coincide. The non-linear, higher-order nature of the field equations arising in non-Einstein theories implies that gravitational waves behave differently than they do in GR. We present some new exact solutions representing gravitational waves (solitons) in a class of theories known as the f(R) gravities. We find that some theories permit modes of arbitrary phase speed, or permit more complicated causal domains. We offer some discussion about black hole nature in f(R) theories and about detection possibilities of sub- or super-luminal gravitational waves.
Guo Chuan Thiang	The differential topology of semimetals and exotic fermions
	In 2015, the elusive Weyl fermion was "discovered" in a topological semimetal. The mathematical characterisation of semimetals turns out to involve deep and subtle results in differential topology, with intriguing links to the notions of Euler structures, torsion of manifolds, and Seiberg-Witten invariants. A proposal for a topological semimetal with torsion charges will be outlined, and is based on the Atiyah-Dupoint-Thomas theory of singular vector fields and the Kervaire semicharacteristic. These ideas can be applied to realise exotic fermionic quasiparticles in condensed matter systems, and to study D-brane charges in string theory. Joint work with Varghese Mathai.
Alessandra Vittorini-Orgeas	Yang-Baxter Solution of Dimers as a Free-Fermion Six-Vertex Model
	Using Yang-Baxter integrability, we study dimers as a free-fermion six-vertex model with crossing parameter λ = π/2. We establish and solve inversion identities on the torus for arbitrary finite size. A one-to-many mapping of vertex onto dimer configurations allows the free-fermion solutions to be applied to the anisotropic dimer model on a square lattice where the dimers are rotated by 45° compared to their usual orientation. In a suitable gauge, the dimer model is described by the Temperley-Lieb algebra with β = cosλ = 0. In the particle representation, the local face tile operators give a representation of the fermion algebra. Finally, we obtain an explicit formula for the counting of the rotated dimer configurations on a finite M × N lattice.
Michael Wheeler	Interplay between Macdonald processes and higher spin vertex models
	The Macdonald processes are specified by (1) a probability measure on sequences of partitions, and (2) a set of Markov kernels with a simple action on this measure. They are built out of the theory of Macdonald polynomials, and encompass many other integrable stochastic processes as special cases. The stochastic six-vertex model is a "twisted" version of the six-vertex model of statistical mechanics, whose Boltzmann weights a,b,c satisfy the relation a=b+c. The latter property allows the model to be interpreted as a discrete-time Markov chain. Recently, some remarkable equivalences have been noticed between the expectation of observables in Macdonald processes and the expectation of observables in the stochastic six-vertex model. These equivalences can be proved by directly comparing integral expressions for such expectations, where they exist. In this talk I will give a conceptual proof of one such equivalence, making use of a Yang--Baxter equation which connects the two processes.
Norman Wildberger	A new framework for relativistic geometry
	We show how rational trigonometry is well suited to framing basic questions about relativistic geometry.
Thomas Wong	Two Friendly Walks in a Sticky Slit
	In previous work we derived an exact solution of two friendly directed walks above a sticky wall with single and double interactions. This models the behaviour of a pair of attracting polymers above an adsorbing surface. In this talk, we extend this to two friendly directed walks in a sticky slab. I'll discuss some difficulties encountered with the analytic approach, the results from numerical analysis, and then compare these results with similar models analysed previously.
Joachim Worthington
Kyle Wright	Geometry on Leibniz algebroids
	The differential geometric structures associated with Lie algebroids, which are compatible with geometric structures on TM, have been received interest lately, due to their relation to local symmetries in gauge theories. Differential geometric structures associated with Courant algebroids on TM ⊕ T*M have also been studied, with applications to several areas of interest to both mathematics and physics. A certain class of Leibniz algebroids are associated with strong homotopy Lie algebras, and have an extended symmetry group. The geometric structures associated to these vector bundles transform nicely under this extended symmetry group. I will discuss the geometry associated to these Leibniz algebroids, some of which have interesting applications in physics, for example T-duality and U-duality.
Luke Yates	Secret Supersymmetry
	The non-appearance of predicted superparticles in high energy particle experiments has placed severe constraints on candidate models of supersymmetry; in particular on the masses of the superpartners of known particles. Drawing on our recent work investigating quadratic deformations of Lie superalgebras we show that for certain extensions of space-time supersymmetries, namely the conformal superalgebra, there are representations without any superpartners. This possibility arises due to a remarkable coincidence of the allowable quadratic extensions of the algebra, where one demands that a generalisation of the PBW theorem holds, and the minimal polynomial identity satisfied by the even subalgebra. Joint work with Peter Jarvis.
Eric Zhou	Face-cubic model on the complete graph
	In this talk, I will describe our recent study on the phase diagram of the general n-component face-cubic model on the complete graph. We focus on the n=2 case as it can be exactly mapped to the Ashkin-Teller model. Using large deviations analysis, we obtain the exact phase diagram. Besides the well-known Ising phase, face-cubic phase and Potts phase, our study indicates the existence of a new ordered phase, which we call super-ordered phase. We note that many of our results can be extended to n>2 cases. Joint work with Timothy Garoni.
Paul Zinn-Justin

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